Related papers: Axisymmetric evolution of Einstein equations and m…
We consider membranes as fluid deformable surface and allow for higher order geometric terms in the bending energy. The evolution equations are derived and numerically solved using surface finite elements. The higher order geometric terms…
We review the problem of describing the gravitational field of compact stars in general relativity. We focus on the deviations from spherical symmetry which are expected to be due to rotation and to the natural deformations of mass…
We analyse the evolution of cosmological perturbations which leads to the formation of large voids in the distribution of galaxies. We assume that perturbations are spherical and all components of the Universe - radiation, matter and dark…
We consider a volume preserving curvature evolution of surfaces in an asymptotically Euclidean initial data set with positive ADM-energy. The speed is given by a nonlinear function of the mean curvature which generalizes the spacetime mean…
We present a numerically stable system of (3+1) evolution equations for the nonlinear gravitational dynamics of quadratic-curvature corrections to General Relativity (Quadratic Gravity). We also report on the numerical implementation of…
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…
A scale--dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies…
We investigate the time evolution of a homogeneous isotropic universe which consists of a perfect gas governed by the Einstein-Euler-de Sitter equations. Under suitable assumptions on the equation of state and assumptions on the present…
In this work we present an approximate solution of the Einstein equations describing a global model for the gravitational field generated by a bounded, self-gravitating stationary and axisymmetric body rotating rigidly with constant angular…
This paper investigates the volume-preserving harmonic mean curvature flow in asymptotically Schwarzschild spaces. We demonstrate the long-time existence and exponential convergence of this flow with a coordinate sphere of large radius…
The theory of evolution equations has been applied in various ways in general relativity. Following some general considerations about this, some illustrative examples of the use of ordinary differential equations in general relativity are…
The concept of smooth deformation of Riemannian manifolds associated with the extrinsic curvature is explained and applied to the FLRW cosmology. We show that such deformation can be derived from Einstein-Hilbert-like dynamical principle…
This paper deals with the global well-posedness of the 3D axisymmetric Euler equations for initial data lying in some critical Besov spaces
We present the first proof-of-principle Cauchy evolutions of asymptotically global AdS spacetimes with no imposed symmetries, employing a numerical scheme based on the generalized harmonic form of the Einstein equations. In this scheme, the…
A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded. All solutions for which curvature invariants approach their limiting values approach…
We establish near-optimal quantitative uniqueness of continuation for solutions of evolution equations vanishing on the lateral boundary. These results were obtained simply by combining existing observability inequalities and energy…
The rigidity of the Positive Mass Theorem states that the only complete asymptotically flat manifold of nonnegative scalar curvature and zero mass is Euclidean space. We study the stability of this statement for spaces that can be realized…
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory…
A generic feature of viable exponential $F(R)$-gravity is investigated. An additional modification to stabilize the effective dark energy oscillations during matter era is proposed and applied to two viable models. An analysis on the future…
General equations of the unified field theory, obtained using the curved and torsional space-time, are presented. They contain only independent geometrical parameters (metric and connections) of the metric-affine space, and describe the…